An Introduction to Fathom

By: Kelli Parker

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Many wonderful programs for statistical analysis have been developed; one of the newest among them is Fathom: Dynamic Data Software by Key Curriculum Press.  Fathom will not only perform data analysis tasks such as creating tables, graphs, and numerical statistics, but it will also run probability simulations, calculate regression lines, test hypotheses, and help with performing and illustrating many other statistical processes. 

Fathom is not only a great tool for statistics classes, though!  It has many included data sets and activities that could be used for other subjects, especially in mathematics.  From working with intersections of lines in Algebra 1, to taking integrals in calculus, Fathom can supplement any classroom with wonderful illustrations and technological demonstrations of important concepts. 

 

This website is meant to be a guide for how to use Fathom for basic tasks and discoveries.  The best resource to guide you with your Fathom use is the Fathom help menu itself, which is found on the menu bar of the program.  The Help menu can link you to all kinds of assistance, from movie demonstrations of how to work with Fathom to individual topic- or subject-based instructions.  Definitely check out the Help menu for any complicated work you need to do!  This resource is here for quick learning that will help get you started exploring in Fathom, and even your students can use this page for their discoveries!  Please check out the activity links at the bottom of the page.

 

Use these bookmarks to find topics quickly!

 

 

Basic_Intro

Box_Plots

Importing_Data

Summary_Statistics

Creating_Tables

Regression_Lines

DotPlots_and_Histograms

Activity_Examples

Scatter_Plots

CityTemperatures_Activity

 

                                                 

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LEARNING ABOUT FATHOM

      

Š      Experience it Yourself!

A great way to experiment with Fathom for the first time is to open a Sample Document.  This will allow you to view many of the different functions of Fathom, as well as see what a finished document can look like.

To Open a Sample Document:

1.  Click “File + Open Sample Document…”

2.  You will see several folders containing sample documents to work with.  Depending on what you want to use Fathom to demonstrate, you will want to look in different folders.  For example, if you want to learn a little more about what Fathom can do, try “Fathom Techniques”, or the “Sample Document” worksheet, which actually allows you to search for a particular topic within all the sample documents that come with the program.
Some of the sample documents contain a collection of data and tell you what to do with it, leaving an open-ended activity for you and/or your class to work through.  Many of these are found in the “Education” and “Teaching Mathematics with Fathom” folders.
Other sample documents are already set up to do simulations, with charts and graphs to record the resulting data entries.  Many of these are found in the “Mathematics” folder, with everything from Algebra 1 simulations of intersecting lines, to probability simulations of drawing marbles with or without replacement.

 

Š      Using Sample Data

Fathom comes with multiple sets of sample data, and most of them are already indicated for a particular use.  These sample data sets are found in the same folders mentioned above. 
Some of the types of data included are:

1.  Census data (including a way to upload current census data from the U.S. Census website)

2.  Scientific observations (occurrences of earthquakes, sunspots, and other natural phenomena, observations of animal behaviors, and chemistry and physics lab data, e.g. changing water temperatures)

3.  Social data (population, GDP, unemployment rates, and even smoking data for multiple continents as well as the whole world)

4.  Sports data (Olympic times and medal winners, football scores, and many others)

5.  Literary and art data (collections documenting the numbers of letters and/or words in famous books, lists of famous artists and painting names)

 

The best way to discover the wonderful resources available in the sample documents and data is to simply click “File” and “Open Sample Documents” and see what you can find!

 


 

 


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WORKING WITH FATHOM: Basic Statistical Analysis

 

Š      Importing Data

Fathom works on the basis of “Collections.”  Any data you bring in to work with gets placed into a collection.  If you have data in an Excel spreadsheet, here is how to capture it:

1.  Highlight all the cells you need.

2.  Select “Edit + Copy” (Ctrl + Copy or Apple + Copy). 

3.  Once in Fathom, click “Collection” on the top menu bar and drag down a new Collection. 

4.  Right click (Ctrl + Click) the Collection box and select Paste Cases. 

 

Data you want to use doesn’t have to be in an Excel spreadsheet; it can be in an online database or another type of worksheet or format.  As long as you can highlight everything you want and Copy it, you should be able to Paste it into a Fathom Collection.

 

Now that your data is in a Collection, it is ready for you to work with.  You can now create tables or graphs, run tests, obtain summary statistics, and do many other things.  First, we’ll focus on the basics of analyzing and manipulating a data set.

 

 

Š      Creating a Table

In order to view your actual data entries, you need to create a Table. 

1.  Click the icon of the Collection you want to work with.

2.  Click the “Table” icon on the menu bar and drag down a table.  Fathom tables function on categories, or “Attributes.”  The data you bring in will any number of attributes, listed as the column headings in your table. 

Below is an example of a table and its attributes:

 

 

3.  You can adjust the size of your table by clicking and dragging the bottom right corner (or any of the other corners).

 

 

Š      Creating Dot Plots and Histograms

One of the easiest ways to look at and do a preliminary analysis of a data set is to get a dot plot or a histogram.  Fathom will do this very easily.  You can select which attribute(s) you want to visualize.  If you choose only one, Fathom will default to a Dot Plot or Histogram.

1.  Click the “Graph” icon on the Menu bar and drag down a Graph box.  (The axes will appear but with no labels.)

2.  Go to your table and select the attribute you want to observe.  Click it and drag it to the graph, and drop it on the axis of your choice.  (For a histogram, drop the attribute on the x- or horizontal axis.)     

 

 

 

 

 

 

Getting an actual count: using a summary table with a histogram

Often it is preferred to have a table of counts instead of a histogram or dot plot.  This is also very easy to do in Fathom.

1.  Click the “Summary” icon on the Menu bar, and drag down a new Summary Table box.

2.  You can get a simple count of the number of items in an attribute (for example, the number of baseball players from each team)
by clicking and dragging that attribute into the summary table.

 

       

 



 

 

              Using a scatter plot for bivariate data

You can compare two attributes from a collection with a scatter plot.
    1.  Click the “Graph” icon on the menu bar and drag down a graph box. 
    2.  Select the attribute you want on the x-axis, and click and drag it onto the horizontal axis of the graph.

3.  Select the other attribute you want to observe, and click and drag it to the vertical (left) axis of the

graph.

 

 

 

Š      Creating Box Plots

A good way to examine the spread of data is to look at a box plot of the data set.  Fathom will let you create a box plot in the same way you create a one-variable histogram or dot plot.

1.  Click the “Graph” icon on the menu bar. 

2.  Drag a graph box down. 

3.  Select the attribute you want to observe and drag it to the horizontal axis of the graph.

4.  The graph will default to a dot plot.  Click the box with the arrows in the top right corner and change the type to a “Box Plot.” 
[You will see all the other types of graphs you can create, as well!]

 

 

 

 

 

Š      Using Summary Tables to Obtain Summary Statistics

As we talk about the spread of data, we also want to consider the median and upper and lower quartiles, i.e a five-number summary, as well as the mean, standard deviation, and other values.  

1.  Click the “Summary” icon on the menu bar and drag down a summary table box.

2.  Click and drag the attribute you want to examine into the table.  You can drop it into the column or row.

 

 

                                   

 

 

Š      Finding a Regression Line

If you already have a scatter plot of two attributes, Fathom can calculate a least-squares line for you.

1.  With your scatter plot already displayed, right- (or Ctrl+) click the graph.

2.  Select “Least Squares Line”.  The line will show up, with its formula below the graph, as well as the r2 value.

 

 

 

 

 

 

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WORKING WITH FATHOM: Activities

 

This section is intended to make you aware of some examples of the types of activities Fathom already has built in.  You’ll be surprised what other subjects Fathom will allow you to work with besides just Statistics!  If you are a Mathematics teacher, then you will want to check out the “Mathematics” Folder when you select “Open Sample Documents” from the File menu.  (The “Teaching Math with Fathom” mostly contains raw data sets with no instructions.)

 

Š      Statistics (in the “Statistics”, not “Mathematics”, folder)

Fathom is great for doing statistics work, from elementary concept investigations to upper level testing and analysis.  The statistics activities available also range from simple exploration to upper level simulations.  Listed below are some of the simpler activities.

¨    Correlation Play: a great introductory activity for students first learning about correlation coefficients.

¨    Quadratic Regression: exploration of alternate “lines” of best fit.

¨    Binomial vs. Normal: good comparison of the binomial and normal probability distributions.

¨    Normal: a chance to discover a great deal about the normal distribution.
 

Š      Probability
The probability activities are a great opportunity to use simulations to solidify some difficult concepts.  A few really good ones are:

¨    Balls Without Replacement: comparing the difference between replacing and not replacing; emphasizing conditional probability.

¨    Black Cards:  how some events affect other events.

¨    Fair Dice: an interesting investigation requiring students to think about important probability concepts.

¨    Buffon Needle: a simulation of the famous problem; very interesting!

 

Š      Algebra 1
These activities allow students to see and manipulate algebra concepts that can sometimes be tricky to understand with non-dynamic graphs and computations.  Students can manipulate sliders and watch how certain parameters affect equations of lines.

¨    Compound Interest: a great manipulation of how principal, interest rate, and period affect total interest.

¨    Rabbit and Frog: developing equations for the speed of two race participants.

¨    Line Intersections: a slider manipulation of slopes and intercepts to determine intersections of two lines.

¨    Slider Functions: determining what a function is given two sliders depicting its behavior; similar to Dynagraphs sketch

¨    Screensaver: a terrific demonstration of parametric equations and how certain values affect them.

 

Š      Calculus

Using these activities can help illustrate and solidify basic concepts of calculus, allowing students to explore why those concepts work.

¨    Derivative Def: illustrating the formula definition of derivative.

¨    Integral And Derivative: an exploration of how derivative and integral are related; Fundamental Theorem of Calculus

¨    Minimization: exercise in finding critical points of curves using the derivative.

Š      Science
Several categories of real-life data students can use mathematical and statistical principles to analyze.

¨    Biology-Mammals: this data allows students to perform some really interesting statistical analysis to find out about animals.

¨    Astronomy-Planet Scan: exploring an exponential function used to analyze real-world objects!

¨    Chemistry and Physics-Heating Water: students can use this data to find a function that describes the cooling pattern of water.

¨    Chemistry and Physics-Moving Ball: observing the effect of initial position and velocity on the path of a ball and the parabolic graph that represents that path.

¨    Earth Sciences-Weather Machine: experimenting with probability of rain or sun on a given day.

¨    Technology-Airplanes: great for aviation fans in your classroom; exploring different associations and graphs.

 

Š      Social Science

More real-life data students can evaluate, from numbers of murders in Chicago, including gender and age of victim and perpetrator, to population and GDP for several other continents and countries.

¨    Canadian Government Debt: offers not only a fathom activity, but links to other great lesson ideas.

¨    SAT GPA: students can analyze associations between gender, gpa, and SAT score.

Š      Sports

These data sets and activities are great for students who don’t care about average heights of buildings and such.  From names and statistics of baseball players to Olympic gold medal winning persons and times.

¨    Baseball 96: lots and lots of baseball statistics; no specific instructions on what to do, but sport-savvy students should have some great ideas.

¨    Summer Olympic Medals: students can consider which countries have earned more gold medals and why.

¨    Bicycling: allows students to work with a real-life example of slope and linear regression.

¨    Mile Records: deals with linear interpolation and extrapolation.

Š      DON’T FORGET YOUR STUDENTS!

Students in your class can generate some great data sets for you.  Have each student fill in their age, height, shoe size, arm length, number of people in their family, and lots of other random facts; they can turn out to be great ways to help your class learn about statistical analysis, using data about them!

 

 

Comparing Temperatures of Two Cities

 

This is a lesson plan and activity I created with a group for a Math Education class.  In this activity, students can explore whether mean or median is a better measure of center, learn how to create dot-plots and box-plots, and practice interpreting what graphs and statistical summaries mean.

 

Click here for Lesson Plan

Click here for Student Worksheet

Click here for Fathom document

 

 

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Thanks for visiting!  Fathom is a wonderful resource you and your students will enjoy using. 

 

Happy Fathoming!!!

 

 

 

Go back to Kelli’s Page

 

 

 

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